An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments?

The time it was when Frank left the playground is; 6:10 PM.

We are given;

Time at which Frank went to the playground; 5:20 p.m

Amount of time that frank played on the slide = 45 minutes

Amount of time that frank swings on the play ground = 5 minutes

Now, we are told that after he played on the slide and swung on the playground, that he went home.

Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.

Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m

Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.

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Answer:

15740000 million dollars in profit in year 4

Step-by-step explanation:

Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.

Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars

Answer:

Given is radius of circle that is 5.2, you just need to find the area of the circle.

To find the are of circle is A=πr2

π value is 3.14 and radius value is 5.2 you just need to square the 5.2, answer will come 27.04

now multiply the πr and 27.04.

the answer will come 84.9 and question says to round to the nearest tenth, that will be 85.

Rounding to the nearest tenth, the surface area of the circle with a 5.2 cm radius is approximately 84.8 cm².

The surface area of a circle can be calculated using the formula:

Surface Area = π * radius²

where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is the distance from the center of the circle to any point on its edge.

Given the radius is 5.2 cm, we can now calculate the surface area:

Surface Area = 3.14159 * (5.2 cm)²

Surface Area = 3.14159 * 27.04 cm²

Surface Area ≈ 84.823 cm²

The surface area represents the total area of the circle's two-dimensional space. In this case, it gives us the total area of the circular region with a 5.2 cm radius.

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Answer:

8/15

Step-by-step explanation:

possibilities/ sample size=16 girls/30 "learners"=8/15

f(x) = 3^x

f(4) = 3^4

f(4) = 3 * 3 * 3 * 3

f(4) = 9 * 9

f(4) = 81

Hope this helps!

Answer:

0.5%

Step-by-step explanation:

Answer:

336 ways

Step-by-step explanation:

Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.

Total number of possible 3-topping pizzas are 336 ways.

In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!

Given that,

Total number of items n = 8

number of picking item k = 3

Now,

p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]

p(8,5) =  [tex]\frac{8!}{(8 -3)!}[/tex]

         = [tex]\frac{8!}{5!}[/tex]

         = [tex]\frac{8.7.6.5! }{5! }[/tex]

         = 8 × 7 ×6

p(8,5) = 336 ways

Hence, Total number of possible 3-topping pizzas are 336 ways.

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Answer:

$25.60

Step-by-step explanation:

1 kg = 1000 grams

peanuts = 6.40 per kg = 0.064 per grams

0.064*400 = 25.6

Answer:

5050

Step-by-step explanation:

we know that 100/2 is 50 and 50 x 100 is 5000

so now another 50 is remaining but we can't multiply but add so

1+2+3+4+5...100 = in simple form= 50x100+50=5050//

Answer: [tex]\Large\boxed{x=6.5}[/tex]

Step-by-step explanation:

Given equation

-9 - (x + 1) = -2 - (3x - 5)

Expand the parenthesis

-9 - x - 1 = -2 - 3x + 5

Combine like terms

-9 - 1 - x = -2 + 5 - 3x

-10 - x = 3 - 3x

Add 3x on both sides

-10 - x + 3x = 3 - 3x + 3x

-10 + 2x = 3

Add 10 on both sides

-10 + 2x + 10 = 3 + 10

2x = 13

Divide 2 on both sides

2x / 2 = 13 / 2

[tex]\Large\boxed{x=6.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: No solution

Distribute the parenthesis

3x-15=2x-10+x

Combine like terms

3x-15=3x-10

This answer has no solution for x.

Answer: B

Step-by-step explanation:

We know N cannot be 0 as the value would not be negative.
We know N cannot be negative as that would make the expression positive.
B is the only answer that works.

Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.

The graph is the one given at the side of the question.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:

y = a(x - 2)² - 1

The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.

y = a(x - 2)² - 1

4 = a(3 - 2)² - 1

a = 5.

Hence the equation is:

y = 5(x - 2)² - 1

Placing it into standard form, we have that:

y = 5(x² - 4x + 4) - 1

y = 5x² - 20x + 19

Hence the coefficients are:

p = 5, q = -20, r = 19.

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Answer:

(-3,1)

Step-by-step explanation:

9x+8y=-19

7x+9y=-12

I'll assume the question is to find the solution to these equations.  The solution will be the point (x,y) where the two lines intersect.  The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.

We can either solve matematically of graph to find the intersection.  I'll do both, and hope the answers are identical.

Matematically

Rearrange either equation to isolate one of the variables (either x or y).  I'll take the second and isolate x:

7x+9y=-12

7x = -9y - 12

x = (-9y - 12)/7

Now use this definition of x in the other equation:

9x+8y=-19

9((-9y - 12)/7) + 8y = -19

(-81y - 108)/7 + 8y = -19

-81y - 108 + 56y = - 133

-25y = -25

y = 1

If y = 1, then:

9x+8y=-19

9x+8(1)=-19

9x = -27

x = -3

The solution is (-3,1)

Graphing

Graph both lines and look for the intersection.  The attached graph shows the lines cross at (-3,1).

The solution, bu both approachjes, is (-3,1)

From the given options we can say that the only one that represents the area of the sector is; A = n/360 * πr²

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

θ/360 * πr²

where;

θ is the central angle of the sector

r is radius

Now, looking at the given options we can say that the only one that represents the area of the sector is;

A = n/360 * πr²

where n is the central angle of the sector

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Answer:

A!

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

54m² - 54m² = 0

Water is 0

There are some ways by which move the steps from sequence and series method like

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

According to the statement

we have to explain the moving steps to change the position of the given three disk from one peg to another.

So, for the solution of this problem

Firstly we know that the sequence and series

An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements.

we have to use the sequence and series method.

So, according to this method

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

So, there are some ways by which move the steps from sequence and series method like

Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.

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The angles and side lengths for both triangles are;

3) A = 36°; B = 54°; C = 90°; a = 7; b = 9.63; c = 4.11

4) A = 64°; B = 26°; C = 90°; a = 1.798; b = 0.88; c = 2

3) From the diagram, we are already given;

B = 54°

C = 90°

a = 7

We know that sum of angles in a triangle is 180° and so;

A = 180 - (90 + 54)

A = 36°

By trigonometric ratios;

b/7 = tan 54

b = 7 * tan 54

b = 7 * 1.376

b = 9.63

7/c = cos 54

c = 7 * cos 54

c = 4.11

4) From the diagram, we are already given;

B = 26°

C = 90°

c = 2

We know that sum of angles in a triangle is 180° and so;

A = 180 - (90 + 26)

A = 64°

By trigonometric ratios;

b/2 = sin 26

b = 2 * sin 26

b = 2 * 0.4384

b = 0.88

a/2 = cos 26

a = 2 * cos 26

a = 1.798

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Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

[tex]f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }[/tex]

.

.

.

Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

[tex]f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }[/tex]

.

.

.

Following the pattern, we can see that for [tex]f^{n}(x)[/tex],

[tex]f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}[/tex]

This applies for n ≥ 1, Expressing f(x) in summation, we have

[tex]\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}[/tex]

Combining ln2 with the rest of series, we have

[tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

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Answer:

  b)  2.45

Step-by-step explanation:

The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.

For the given points ...

  [tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]

The distance between x and y is ...

  [tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]

The difference between the 6th term and the 9th term of the sequence is 135

Given that the nth term is;

3n² + 11

For the 6th term, the value of n is 6

Let's solve for the 6th term

= 3( 6)^2 + 11

= 3 × 36 + 11

= 108 + 11

= 119

For the 9th term, n = 9

= 3 (9)^2 + 11

= 3( 81) + 11

= 243 + 11

= 254

The difference between the 6th and 9th term

= 254 - 119

= 135

Thus, the difference between the 6th term and the 9th term of the sequence is 135

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Answer:

Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.

If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

Using Pythagoreans theorem formula

a²=b²+c²

Where:

c=16 feet

a=40/2=20 feet

Hence:

20²=b²+16²

b²=20²-16²

b²=400-256

b²=√144

b=12

2b=12×2

2b=24 feet

Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

The complete question is are:

A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?

a. 34 feet

b. 46 feet

c. 24 feet

d. 30 feet

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The length of one edge of the cube exists 6 centimeters.

The lateral surface area of a cube exists

[tex]$A=4 a^{5}$[/tex]

where a stands the length of one edge of a cube.

It exists given that the lateral surface area of the square stands at 144 square centimeters.

Substitute A = 144 in the above formula.

[tex]$144=4 a^{2}[/tex]

Divide both sides by  4.

[tex]$36=a^{2}[/tex]

Taking square root on both sides.

[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]

6 = a

The length of one edge of the cube exists 6 centimeters.

Therefore, the correct answer is option c. 6 cm.

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The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system of equation

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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Answer:

Positive

Step-by-step explanation:

5a < 2a

Divide 2 on both sides

5/2a < a

Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)